Don't play too hard.
Some good suggestions here. I'll add a few of my own... been playing bass since 1980 so I figure I know a thing or two.
The tone you're describing is not my usual tone, but I do go for it sometimes when I'm in a metal mood.
First, set up the bass with new strings (roundwound), detuned somewhat, with low action. A little fret buzz helps with the growl.
Finger technique is very important to this tone. Don't play too hard! Try playing very lightly with your fingers near the middle pickup, or maybe closer to the bridge. The motion is hard to describe, and varies a lot from player to player. Some people have more of a "pluck" and some have more of a "smack". For an aggressive nu-metal sound I'll suggest that you try to very lightly "smack" the string instead of plucking it. Your finger should be relaxed and poised above the string; don't rest on the string before playing the note, and don't pull on the string. The neutral position is with your fingers hovering, relaxed, about an inch from the strings. The thumb can rest on a pickup edge if you like. To play a note, you just flick your fingertip in (towards your thumb or palm) and let it glance off the string as it goes by. You don't want to hook on to the string and yank it, so keep the finger relaxed throughout the movement. Once you get the hang of this, you can play pretty fast without getting tired.
It takes a while to get the hang of that. To make recordings in the meantime, play lightly with a pick.
As for gear:
Pickups mattter. A J-bass or P/J combination will work. If you have 2 pickups, use both. The interaction of the pickups helps scoop out some of the midrange, which is crucial to this tone. You can sort of fake it with a P-bass but it takes some radical EQ. Active pickups can help because they tend to be brighter.
EQ. Try severely boosting the upper mids / lower treble - somewhere between 3k and 6k. If you're running direct, kill everything over about 8k - it just sounds tinny and weird to me. Boost the lows too, below about 150 Hz. Or you could start with the lows and highs flat, and cut out the midrange.
Don't be afraid to boost or cut a LOT. This tone depends on EQ, whether it comes from the bass (active EQ), the amp, the DI, whatever. I've found that the SansAmp Bass DI is ready-made for this tone.
Optional: Maybe a touch of distortion, if you have something that's subtle and doesn't kill the low end. Most guitar pedals aren't good for this. A RAT will do if you boost the lows afterward. You're not looking for a big fuzzy sound, just a little more edge, so set the overdrive very low and compensate with the output level.
Compression helps. If you have a compressor to play with, try it. Especially if your finger technique isn't quite happening yet, it'll help smooth out your dynamics. And combined with bright EQ, it'll also help bring out the growly sustain.
Hope that helps somebody!
